On Zeros of Dirichlet L-Functions and the Least Prime in an Arithmetic Progression

Triantafyllos Xylouris (University of Bonn)

Thursday 21 April 2011, 15.00, b-it 1.25 (cosec meeting room)

Let a and q be coprime natural numbers. In 1944, Linnik proved that the least prime in an arithmetic progression a mod q is less then Cq^L. Since then the admissible value for the constant L has been improved several times, lastly by Heath-Brown in 1992 to L=5.5. In his article Heath-Brown describes several improvement potentials for his paper. Building on these potentials we improve the intermediate results concerning zeros of Dirichlet L-Functions and finally the admissible constant to L=5.0. This talk serves to give an introduction into this topic and our work.